Asymptotic localization of stationary states in the nonlinear Schrödinger equation

Shmuel Fishman; Alexander Iomin; Kirone Mallick

doi:10.1103/PhysRevE.78.066605

Asymptotic localization of stationary states in the nonlinear Schrödinger equation

Shmuel Fishman
, Alexander Iomin
, Kirone Mallick

Technion - Israel Institute of Technology
Institut Pierre Simon Laplace, CNRS and CEA

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

The mapping of the nonlinear Schrödinger equation with a random potential on the Fokker-Planck equation is used to calculate the localization length of its stationary states. The asymptotic growth rates of the moments of the wave function and its derivative for the linear Schrödinger equation in a random potential are computed analytically, and resummation is used to obtain the corresponding growth rate for the nonlinear Schrödinger equation and the localization length of the stationary states.

langue originale	Anglais
Numéro d'article	066605
journal	Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume	78
Numéro de publication	6
Les DOIs	https://doi.org/10.1103/PhysRevE.78.066605
état	Publié - 1 déc. 2008
Modification externe	Oui

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10.1103/PhysRevE.78.066605

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title = "Asymptotic localization of stationary states in the nonlinear Schr{\"o}dinger equation",

abstract = "The mapping of the nonlinear Schr{\"o}dinger equation with a random potential on the Fokker-Planck equation is used to calculate the localization length of its stationary states. The asymptotic growth rates of the moments of the wave function and its derivative for the linear Schr{\"o}dinger equation in a random potential are computed analytically, and resummation is used to obtain the corresponding growth rate for the nonlinear Schr{\"o}dinger equation and the localization length of the stationary states.",

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AU - Iomin, Alexander

AU - Mallick, Kirone

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N2 - The mapping of the nonlinear Schrödinger equation with a random potential on the Fokker-Planck equation is used to calculate the localization length of its stationary states. The asymptotic growth rates of the moments of the wave function and its derivative for the linear Schrödinger equation in a random potential are computed analytically, and resummation is used to obtain the corresponding growth rate for the nonlinear Schrödinger equation and the localization length of the stationary states.

AB - The mapping of the nonlinear Schrödinger equation with a random potential on the Fokker-Planck equation is used to calculate the localization length of its stationary states. The asymptotic growth rates of the moments of the wave function and its derivative for the linear Schrödinger equation in a random potential are computed analytically, and resummation is used to obtain the corresponding growth rate for the nonlinear Schrödinger equation and the localization length of the stationary states.

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DO - 10.1103/PhysRevE.78.066605

M3 - Article

AN - SCOPUS:58149271157

SN - 1539-3755

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JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

IS - 6

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Asymptotic localization of stationary states in the nonlinear Schrödinger equation

Résumé

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